Chapter 11: Q. 355 (page 1069)

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 14 a + 33$

Short Answer

Expert verified

The factored form of the polynomial is $(a + 11) (a + 3)$ .

Step by step solution

Step 1. Given Information

We are given a polynomial,

$a^{2} + 14 a + 33$

Step 2. Factorizing the polynomial

Using the product of $a c$ method in factorizing the polynomial of form $a x^{2} + b x + c$ , we get

$11 \times 3 = 33 11 + 3 = 14$

So, Splitting the middle term,

localid="1644849982369" $a^{2} + 14 a + 33 = a^{2} + 11 a + 3 a + 33$

Grouping terms, we get

localid="1644849962131" $a^{2} + 14 a + 33 = (a^{2} + 11 a) + (3 a + 33)$

Factoring out GCF from groups, we get

localid="1661956442984" $a^{2} + 11 a + 3 a + 33 = a (a + 11) + 3 (a + 11)$

Again, factoring out GCF, we get

localid="1644850003709" $a^{2} + 14 a + 33 = (a + 11) (a + 3)$

Step 3. Checking the factorization

Multiplying the factors,

$(a + 11) (a + 3) = a^{2} + 14 a + 33 a (a + 3) + 11 (a + 3) = a^{2} + 14 a + 33 a^{2} + 3 a + 11 a + 33 = a^{2} + 14 a + 33 a^{2} + 14 a + 33 = a^{2} + 14 a + 33 L H S = R H S$

Hence the factorization is correct.

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In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 14 a + 33$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorizing the polynomial

Step 3. Checking the factorization

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In the following exercises, factor each trinomial of the form x2+bx+c.a2+14a+33

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factorizing the polynomial

Step 3. Checking the factorization

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Pure Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .
$a^{2} + 14 a + 33$